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( )René Descartes (1596 – 1650) Cartesian I can place 2 

number lines 

Cartesian coordinate number lines 

one perpendicular 

system

perpendicular to the other so h   h   h  f that the path of the flying bird can be set   

What is Analytical geometry?

A systematic study of geometry by the use of algebraby the use of algebra

La Geometric published in 1637

Coordinates of a pointY3

ctio

n

Y-axis : Y’OY

1

2

vedirec

X-axis : X’OX

XX’ O

1 2 3 41234

1

+vX axis : X OX

Origin

1 2 3 4

+ve direction

-1-2-3-4

-1

ection

Y’-ve direction

-2

-3 -ve

dire

Y 3 -

di tcoordinatesAbscissa

Ordinate

N

M

Q d tQuadrantsY

( )( )

III(+,+)(-,+)

XX’ OIII

III IVY’

(-,-) (+,-)Y

E lExampleY

3

1

2

(2,1)Abcissa

XX’ O

1 2 3 41234

1

1 2 3 4-1-2-3-4

-1Ordinate

Y’

-2

-3

(-3,-2)

(?  ?)Y 3 (?, ?)

Points on the axes

Image of a pointImage of a point

N

MO

T   i   h  i   f    i   b  

O

To write the image of a point about th   i   l     b     

To write the image of a point about the y‐axis replace x by – x  the x‐axis replace  y by  – y. 

Image about the origin

To write the image of a point about the origin replace x by – x and y by – y y y y

Example

If th b i f i t If the abscissa of a point is three times the ordinate then

Gi diti i Given condition is

Example

If the abscissa of the point If the abscissa of the point is square of its ordinate then

Given condition is Given condition is

The point (3, 2) moves a distance 5 units in the negative direction of gthe x-axis. From its new position it turns to the direction of the turns to the direction of the negative y-axis and moves a distance 7 units Write the new distance 7 units. Write the new position of the point

2   32   3M2

5N

5

A point lies on the x-axis at a distance 3 units from the point distance 3 units from the point (- 2, 0). The position of the point iis

Example Image of about the x axis isabout the x-axis isabout the y-axis is

is the image ofabout the origin

ExampleThe image of (x, y) about the g ( , y)x-axis and y-axis respectively are (2 - 3) and (- 2 3) Find are (2, 3) and ( 2, 3). Find x and y.image about x axis is (2 3)image about x-axis is (2, - 3)image about y-axis is (- 2, 3)

y = 3

g y ( , )

x = 2 (2, 3)

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